Universal attractors for the Navier-Stokes equations of compressible and heat-conductive fluid in bounded annular domains in R-n

This paper is concerned with the dynamics for the Navier-Stokes equations f or a polytropic viscous heat-conductive ideal gas in bounded annular domain s Omega (n) in R-n (n = 2, 3). One of the important features of this proble m is that the metric spaces H-(1) and H-(2) we work with are two incomplete metric spaces, as can be seen from the constraints theta > 0 and u > 0, wi th theta and u being absolute temperature and specific volume respectively. For any constants delta (1), delta (2), delta (3), delta (4), delta (5) sa tisfying certain conditions, two sequences of closed subspaces H-delta((i)) subset of H-(i) (i = 1, 2) are found, and the existence of two (maximal) u niversal attractors in H-delta((i)) and H-delta((2)) is proved.